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Scoring rules for statistical models on spheres. (English) Zbl 1463.62158

Summary: We introduce a novel class of strictly proper scoring rules for statistical models on spheres that does not require the calculation of normalizing constants. The class contains the Hyvärinen scoring rule investigated by K. V. Mardia et al. [“Score matching estimators for directional distributions”, Preprint, arXiv:1604.08470].

MSC:

62H11 Directional data; spatial statistics
62F10 Point estimation

Software:

hgm R

References:

[1] Dawid, A. P., The geometry of proper scoring rules, Ann. Inst. Statist. Math., 59, 77-93, (2007) · Zbl 1108.62009
[2] Ehm, W.; Gneiting, T., Local proper scoring rules of order two, Ann. Statist., 40, 609-637, (2012) · Zbl 1246.86013
[3] Hyvärinen, A., Estimation of non-normalized statistical models by score matching, J. Mach. Learn. Res., 6, 695-709, (2005) · Zbl 1222.62051
[4] Kume, A.; Wood, A. T.A., Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants, Biometrika, 92, 465-476, (2005) · Zbl 1094.62063
[5] Mardia, K. Kent,J., Laha, A., 2016. Score matching estimators for directional distributions. arXiv:1604.08470; Mardia, K. Kent,J., Laha, A., 2016. Score matching estimators for directional distributions. arXiv:1604.08470
[6] Mardia, K.; Jupp, P., Directional statistics, (2000), Wiley Chichester · Zbl 0935.62065
[7] Nakayama, H.; Nishiyama, K.; Noro, M.; Ohara, K.; Sei, T.; Takayama, N.; Takemura, A., Holonomic gradient descent and its application to Fisher-Bingham integral, Adv. Appl. Math., 47, 639-658, (2011) · Zbl 1226.90137
[8] Parry, M.; Dawid, A. P.; Lauritzen, S., Proper local scoring rules, Ann. Statist., 40, 561-592, (2012) · Zbl 1246.62011
[9] van der Vaart, A., Asymptotic statistics, (1998), Cambridge University Press · Zbl 0910.62001
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